Method and system for media initialization via data sharing

ABSTRACT

A method, apparatus, and computer-readable medium estimate media performance on advertising space inventory. The method selects at least one media cell that shares one or more common attributes with a target media cell. The method subsequently estimates mean revenue per impression (RPI) of the selected media cell, and then defines an initial estimate of a RPI of the target media cell based on the estimated RPI of the selected cell. The method computes the RPI of the target media cell by combining the initial RPI estimate for the target media cell with performance data associated with the target media cell.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation of and claims the benefit of priorityto U.S. patent application Ser. No. 12/314,499, filed Dec. 11, 2008 nowU.S. Pat. No. 8,301,497, which claims the benefit of priority to U.S.Provisional Patent Application No. 61/045,914, filed Apr. 17, 2008. Thecontents of the above-referenced applications are expressly incorporatedherein by reference to their entireties.

DESCRIPTION OF THE INVENTION

1. Field of the Invention

The present disclosure relates to placement of media on advertisingspace inventory on an electronic medium, and more specifically, toestimating media performance on the advertising space inventory.

2. Background of the Invention

Online advertising has become a billion dollar industry in today'sdigital content-driven economy. The portability of digital content usingmobile computing devices, such as smart phones and media players, hasexpanded the reach of online advertisers beyond traditional personalcomputer users. Advertisers and publishers of online content, however,desire accurate estimates of the performance of advertisements, such asthe performance of a particular advertisement associated with a specificlocation on a website, in order to ensure effective ad placement.

Accurate and cost-effective performance estimates for a particularadvertisement on a specific location of a particular website may rely onhistorical performance data associated with the particular advertisementor the particular website. For example, performance estimates of theparticular advertisement on the specific website location can be basedon that advertisement's performance on similar websites, oralternatively, on the performance of similar advertisements on thespecific location of the particular website. While these techniques arecost-effective and provide reasonable performance estimates, they arealone insufficient to estimate the performance of an advertisement orwebsite that lack historical performance data.

In such instances, data sharing can be coupled with historical data toprovide a cost-effective and accurate estimate of advertisementperformance on a segment of advertising space inventory. But, datasharing techniques may require some knowledge of an “average”performance of a similar set of advertisements on the specific locationon a website, or alternatively, of an “average” performance of theadvertisement on a similar set of websites. In practice, computing anaccurate and unbiased determination of these “average” performancemetrics may be difficult to implement.

Therefore, an improved approach is needed to compute a measure of mediaperformance for data sharing applications.

SUMMARY OF THE INVENTION

Consistent with embodiments of the present invention, a method forpredicting media performance on a segment of advertising space inventoryselects at least one media cell that shares one or more commonattributes with a target media cell. The method then estimates a meanrevenue per impression for the selected media cell and subsequentlypredicts a revenue per impression of the target media cell from theestimated mean revenue per impression of the selected media cell.

Consistent with embodiments of the present invention, an apparatusincludes a storage device and a processor coupled to the storage device.The storage device stores a program for controlling the processor, andwherein the processor, being operative with the program, is configuredto select at least one media cell that shares one or more commonattributes with a target media cell. The processor is configured toestimate mean revenue per impression for the selected media cell andthen subsequently predict a revenue per impression of the target mediacell from the estimated mean revenue per impression of the selectedmedia cell.

Consistent with embodiments of the present invention, a computerreadable medium includes comprising a set of instructions that, whenexecuted on a processor, perform a method for estimating mediaperformance on advertising space inventory. The method selects at leastone media cell that share one or more common attributes with a targetmedia cell. The method the estimates a mean revenue per impression forthe selected media cell and subsequently predicts a revenue perimpression of the target media cell from the estimated mean revenue perimpression of the selected media cell.

It is to be understood that both the foregoing general description andthe following detailed description are exemplary and explanatory only,and are not restrictive of the invention. Further, the accompanyingdrawings, which are incorporated in and constitute a part of thisspecification, illustrate embodiments of the invention and together withthe description, serve to explain principles of the invention.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a flowchart of an exemplary method for predicting mediaperformance on advertising space inventory, according to an embodimentof the present invention.

FIG. 2 is a flowchart of an exemplary method for selecting media cellsthat share one or more common attributes with a target media cell,according to an embodiment of the present invention.

FIG. 3 is a flowchart of an exemplary method for estimating a meanrevenue per impression (RPI) of media cells using RPI distributionmodeling, according to an embodiment of the present invention.

FIG. 4 is a graph of an exemplary RPI distribution for a media cell,according to an embodiment of the present invention.

FIG. 5 is a flowchart of an exemplary method for computing mean RPI formedia cells having insufficient data for RPI distribution modeling,according to an embodiment of the present invention.

FIG. 6 is a flowchart of an exemplary method for predicting a RPI of atarget media cell using data sharing, according to an embodiment of thepresent invention.

FIG. 7 is a graph of an exemplary predicted RPI for a target media cell,according to an embodiment of the present invention.

FIG. 8 is a diagram of an exemplary computer system that implementsembodiments of the present invention.

DESCRIPTION OF THE EMBODIMENTS

Reference will now be made in detail to embodiments of the invention,examples of which are illustrated in the accompanying drawings. The samereference numbers will be used throughout the drawings to refer to thesame or like parts.

Notably, as used herein, the terms “media,” “advertisement,” and “ad”are meant to include any content, including information or messages, aswell as Web banners, product offerings, special non-commercial orcommercial messages, or any other displays, graphics, video, or audioinformation.

Further, the term “tract,” as used herein, generally refers to a portionof advertising space inventory defined by a plurality of attributes,including, but not limited to, a website, a slot size on that website,and a segmentation model associated with the website and slot size.Moreover, in this application, the term “media cell” or “cell” generallyrefers to an intersection of a particular media and a particular tractof advertising space inventory.

However, the “media cell” or “cell,” as used herein, is not limited tosuch definitions, and in general, the “media cell” or “cell” may bedefined as an intersection of a particular media and any number ofabstract properties of advertising space inventory apparent to oneskilled in the art. The definitions of other terms used throughout thisapplication, such as “revenue model,” “leadback model,” “segmentationmodel,” and terms related to these terms are set forth more fully below.

Furthermore, in this application, the use of the singular includes theplural unless specifically stated otherwise. In this application, theuse of “or” means “and/or” unless stated otherwise. Furthermore, the useof the term “including,” as well as other forms such as “includes” and“included,” is not limiting. In addition, terms such as “element” or“component” encompass both elements and components comprising one unit,and elements and components that comprise more than one subunit, unlessspecifically stated otherwise. Additionally, the section headings usedherein are for organizational purposes only, and are not to be construedas limiting the subject matter described.

1. Introduction to Performance Prediction and Data Sharing

Efficient performance prediction requires an accurate initial estimateof a performance of a media on a particular tract of advertising spaceinventory. Such an initial estimate, if reasonably accurate, helpsreduce a number of impressions that a media must be shown in order toobtain a statistically accurate estimate of the performance of the mediaon the tract of advertising space inventory. The process of determiningthe optimal number of required impressions is referred to as “learning.”

In an embodiment, an exemplary learning strategy schedules a certainminimum number of impressions of a target media on a pre-defined set ofinventory to obtain reasonable estimates, or grades, for that media.This strategy, though effective, can be expensive. Alternatively,improvements to the initial performance estimates can be obtained usingavailable historical data related to the target media.

However, in situations where historical data is unavailable for thetarget media (or campaign), data sharing can provide an initial revenuerate estimate of a specific target media on a particular tract ofadvertising space inventory, i.e., a target media cell. Data sharing isbased on an intuitive idea that reasonable expectations can be derivedabout how a media will perform on some inventory by considering how thatsame media has performed on other inventory, or how other medias fromthe same or similar campaigns have performed on that same inventory.

Different sources of similarity between cells, i.e., different sharedcharacteristics or relationships, can provide various data-sharingopportunities. Example of commonalities or relationships between cells,referred to as “attributes,” which provide data sharing opportunitiescan include, but are not limited to:

-   -   (i) a common website;    -   (ii) a common segmentation model;    -   (iii) a common slot size;    -   (iv) a common tract (i.e., a website-slot-segment definition);    -   (v) a common leadback model;    -   (vi) a common revenue model;    -   (vii) a common media or campaign;    -   (viii) a common run-time definition (RTD) identifier; and    -   (ix) medias from campaigns having a common industry.

The various relationships that can be used for data sharing purposes canbe classified, generally, into three broad categories: segment effects,campaign effects, and attribute effects. Segment effects generally arisewhen cells share inventory properties, including but not limited to acommon website, a common slot size, a common segment model, and a commontract (i.e., a combination of a common website, slot size, and segmentmodel). Campaign effects generally arise when cells share specific mediaidentities, including but not limited to common campaign identifiers andcommon media identifiers. Attribute effects generally arise when cellsshare more general media properties, including but not limited to acommon leadback model and a common revenue model.

Segment effects correlate the performance of different medias on thesame segment of advertising space inventory. For example, predictions ofmedia performance using data from other campaigns on the same websiteslot are based on segment effects. Intuitively, a likelihood that avisitor to one website will click on or convert a particular media maybe greater than that of a visitor to a different website. As such, anaverage performance of a media on a higher-converting website may behigher than an average performance of that media on a lower-convertingwebsite. In general, such correlations are captured by segment effects.Thus, segment effects can contribute to performance predictions fornewly-launched campaigns through data sharing.

Attribute effects correlate similarities in performance of differentmedias having shared attributes or properties. For example, attributeeffects account for a portion of a performance estimate that resultsfrom specific characteristics of a media, such as a particular revenuemodel and a particular leadback model. Attribute effects that resultfrom the targeting of a media to particular users, such as the leadbackmodel, may be referred to as “targeting effects.” As described above forsegment effects, attribute effects can contribute to performancepredictions for newly-launched campaigns.

Campaign effects describe the performance of different cells belongingto the same campaign. For example, campaign effects account for thatportion of a media's performance estimate attributable to a strength ofa campaign. Such effects may arise from a tendency of some campaigns toperform better than other campaigns across a variety of websites. Thegeneral term “campaign effect” also encompasses more specificcorrelations, such as those of a single media or campaign performancesegment (CPS) across different websites. In certain embodiments,campaign effects are based on the past performance of medias from asingle campaign, so campaign effects cannot contribute to performancepredictions for newly-launched campaigns through data sharing.

An underlying premise of data sharing is that similar cells will havesimilar performance, as measured by revenue per impression (RPI), i.e.,revenue earned from events resulting from a number of impressionsgathered by a cell divided by the number of impressions. However, suchan underlying premise may appear counter-intuitive, especially in viewof the wide disparity in media cost-per-unit (CPU) and media conversionrates across an advertising network.

In an embodiment, a “conversion” of a media represents a predefinedaction that a publisher of the media desires a consumer to complete. Forexample, a conversion of a particular media on a segment of advertisingspace inventory can include, but is not limited to, making a purchasefrom a retailer associated with the media, registering for an emailnewsletter, and requesting sales information. In such an embodiment, aconversion rate of the media represents a quotient of a number ofconversions received by the media during some period and a number ofimpressions of that media shown during that period.

In general, the conversion rate of a media in a particular campaign isinversely proportional to the cost-per-unit (CPU) of that media in theparticular campaign. As such, as an anticipated conversion rate of themedia in the campaign decreases, an anticipated CPU of the media in thecampaign increases. Campaigns may be priced in this fashion to provide acompetitive RPI on an advertising network. Therefore, while largedifferences exist between the CPUs of media of different campaigns andbetween the conversion rates of different cells, much less variationexists between the resulting RPIs of these cells.

However, such a generalization does not imply that all media on aparticular tract of advertising inventory have identical RPIs. While awide range of RPIs can exist among different cells, the use of anaverage RPI of a class of cells as an initial estimate of a RPI of a newcell provides a useful starting point for predicting the performance ofthat new cell. As such, observations of performance of a group of cellscan, in various embodiments, be used to generate performance predictionsfor cells with no history. Furthermore, data sharing can be used toenhance the performance estimates for such new cells by blendingcell-specific history with data from related cells.

Therefore, an exemplary approach to estimate an initial performance of atarget cell through data sharing includes:

-   -   (i) identifying a set of peer cells similar to the target cell;    -   (ii) estimating an average RPI of those peer cells; and    -   (iii) using the average as the estimated RPI of the target cell,        and the variance of the estimate as the variance.

In such an approach, the set of peer cells may share a common factor ora combination of common factors with the target cell, including but notlimited to one or more attribute effects, segment effects, and campaigneffects. Furthermore, the target cell itself may be included within theset of peer cells, or alternatively, the target cell may be excludedfrom the set of peer cells. If the target cell were included within theset of peer cells, historical data associated with the target cell willbe considered in the calculation of the estimated average cell RPI. Inan embodiment, the target cell may be included within the identifiedpeer cells if the historical data associated with the target cell meetsa data sufficiency criteria based on, for example, a quantity or qualityof available historical data.

2. Average Cell RPI, Aggregated Cell RPI, and Scheduling Bias

However, care must be taken in estimating an average RPI of a set ofpeer cells. In some approaches, an aggregated RPI of the peer cellsserves as an initial estimate of the average RPI of the peer cells. Theaggregated RPI of the impressions awarded to the peer cells can, forexample, be calculated by dividing a revenue earned from those cells bythe number of impressions awarded to those cells, as follows:

$\begin{matrix}{{{RPI}_{aggregated} = {\frac{Revenue}{Impressions} = \frac{\sum{a_{k}c_{k}}}{\sum n_{k}}}},} & (1)\end{matrix}$where k is an index of a cell within the peer cells, a_(k) and n_(k)are, respectively, the number of events and impressions that have beenobserved at cell k, and c_(k) is the cost-per-unit (CPU) of the mediafrom that cell.

The aggregated RPI, as computed above, may serve as an “average” RPI ofthe set of cells, and hence, may estimate an earning potential of a new,untried cell. However, the aggregated RPI may fail to estimateaccurately the average RPI of the peer cells due to a bias introducedduring the optimization process.

As previously described, one goal of the optimization process is todetermine which medias perform well and which perform poorly, and thento show the high-performing medias more frequently on the segment ofadvertising space inventory. If the optimization process is successful,then an average revenue earned by the medias shown on some inventoryshould be higher than a revenue that could be earned by randomlyrotating the medias. The following example illustrates the operation ofthe optimization process and demonstrates how scheduling bias can beintroduced into the process.

In one embodiment, for example, an accurate assessment of a performanceof a cell can be determined after that cell accumulates 1,000impressions. Further, in this embodiment, eight competing media arelaunched on a given tract of advertising space inventory for a testperiod during which each media is awarded at least 1,000 impressions. Atthe end of the test period, a revenue per thousand impressions (RPM,i.e., a revenue per impression (RPI) multiplied by 1,000) is calculatedfor each of the eight media based on the number of impressions receivedby each media, as described in Table 1. Further, the total revenueearned by each of the media is computed as a product of the RPM for themedia and the number of thousands of impressions received by the media.Table 1 lists the revenue-per-thousand-impressions (RPM), total numberof impressions, and total revenue earned by each of the eight samplemedia, consistent with this embodiment.

TABLE 1 Ad RPM Impressions Revenue 1 $0.30 1000 $0.30 2 $0.50 1000 $0.503 $0.75 1000 $0.75 4 $0.90 2000 $1.80 5 $1.00 10000 $10.00 6 $1.25 20000$25.00 7 $1.75 100000 $175.00 8 $2.50 5000 $12.50 Avg = $1.12 Σ = 140000Σ = $225.85

In the embodiment of Table 1, Ads 1, 2, and 3, which respectively havethe lowest RPM among the eight media, would not receive impressionsoutside of the testing period. Further, Ad 8 appears to be performingstrongly with a RPM of $2.50. However, with only 5,000 impressions, Ad 8appears to be targeted to a relatively small audience (i.e., Ad 8 istightly-targeted) and as such, would be ineligible for most impressionson the sample tract. Ad 7, with $1.75 RPM and 100,000 impressions, isboth a strong performer and broadly targeted, and as such, would receivethe most impressions through the optimization process.

The average RPM of these individual media on the tract (e.g., anarithmetic mean RPM of the cells) is $1.12, and using data sharing, thisaverage RPM could be an accurate prediction for the RPM of a new,unknown media on this tract. In contrast, an aggregated RPM of thistract is calculated by dividing the total revenue earned by theimpressions served:

$\begin{matrix}\begin{matrix}{{RPM}_{aggregated} = {\frac{Revenue}{Impressions} \times 1000}} \\{= {\frac{{\$ 225}{.85}}{140000} \times 1000}} \\{= {{\$ 1}{.61}}}\end{matrix} & (2)\end{matrix}$

The aggregated RPM of $1.61 is higher than the average RPM of theindividual cells. Such a result is both expected and desired in thisembodiment, as the optimization process successfully identified andpreferentially displayed the higher-performing medias of the tract.Therefore, in this embodiment, the effective operation of theoptimization process results in a discrepancy between aggregated andaverage RPM.

In an additional embodiment, a discrepancy between aggregated andaverage RPM can result from the fact that campaigns have predeterminedbudgets. For example, a campaign with a large budget may have a greaterchance of receiving impressions than a comparable campaign with asmaller budget. As such, the campaign with the large budget may have alarger contribution to aggregated RPM than the comparable campaign withthe smaller budget. In such a fashion, predetermined budgets fordifferent campaigns may bias, either positively or negatively,performance of a website on which these campaigns are shown. Suchdiscrepancies between aggregated and average RPM may be referred to as“scheduling bias.”

Data sharing predictions that use aggregated RPI (or RPM) as an estimatefor average cell RPI may be too optimistic, thus resulting in new cellsbeing overvalued relative to established cells, e.g., existing cellsthat have gathered a substantial number of impressions and/or actions.If this leads to newer cells winning inventory that ideally should havegone to established cells, the result is lower overall revenue for theadvertising network.

In practice, the calculation of a more precise RPI of performance-basedcells and an average cell RPI may be difficult to perform. However, insuch situations, the aggregated cell RPI may be relativelystraightforward to calculate. Therefore, even in view of its inherentscheduling bias, the aggregated cell RPI may be used to estimate anaverage cell RPI in data sharing approaches.

3. Methods and Systems for Estimating Media Performance UsingDistribution Modeling

FIG. 1 illustrates an exemplary method 100 for estimating mediaperformance on advertising space inventory that probabilistically modelsaverage cell RPI with limited scheduling bias, according to anembodiment of the invention. In step 102, at least one media cell isselected that shares one or more common attributes with a target mediacell, thereby forming a set of selected media cells. These commonattributes can include, but are not limited to: a common tract ofadvertising space inventory, a common revenue model, a common slot size,a common segmentation model, a common media, a common industry campaign,or any additional or alternate attribute apparent to one of skill in theart.

In an embodiment, the set of selected media cells can include a singlemedia cell that shares one or more common attributes with the targetmedia cell. However, in an additional embodiment, step 102 can selectany plurality of media cells that share one to more common attributeswith the target media cell without departing from the spirit or scope ofthe present invention.

In an embodiment, the target media cell represents a media, including,but not limited to, an advertisement displayed on a target tract ofadvertising space inventory. Furthermore, each of the selected mediacells represents a media, including, but not limited to, anadvertisement displayed on a selected tract of advertising inventory.However, the target and selected cells are not limited to suchrepresentations, and in additional or alternate embodiments, the targetmedia cell and each selected media cell can respectively represent anintersection of a particular media with any additional or alternateproperty of advertising space inventory.

Step 104 estimates a mean revenue per impression (RPI) of the set ofselected media cells. In an embodiment, step 104 estimates the mean RPIof the selected media cells using a mathematical model of an underlyingcontinuous probability distribution for the RPI of the selected mediacells, as described below in reference to FIG. 3. As such, thecalculation of the estimated mean RPI of the set of selected media cellsin step 104 may reduce or eliminate the scheduling bias that may beassociated with estimates of mean RPI, such as an aggregate cell RPI.

Furthermore, in an embodiment, step 104 can adjust the estimated meanRPI of the set of selected media cells to account for a leadback modelassociated with the target media cell. For example, step 104 can adjustthe estimated mean RPI of the set of selected media cells to account foran audience leadback model or an advertiser leadback model of the targetmedia cell.

Step 106 predicts a revenue per impression (RPI) of the target mediacell based on the estimated mean RPI of the set of selected media cells.In an embodiment, step 106 first defines an initial estimate of the RPIof the target media cell based on the estimated mean RPI of the set ofselected media cells. Step 106 then predicts the RPI for the targetmedia cell based on at least the initial estimate. In an embodiment,step 106 computes the RPI of the target media cell by blending theinitial estimate of the RPI of the target media cell with data onhistorical performance of the target media cell.

In an embodiment, the selected media cells and the target media cellshare both a common tract of advertising space inventory and a commonrevenue model. In this embodiment, the RPI of the target media cellpredicted by step 106 corresponds to a specific tract of advertisingspace and a specific revenue model. However, in an additionalembodiment, a target media cell may be associated with multiple revenuemodels. As such, the processes described above in reference to FIG. 1can predict multiple RPIs for a target media cell, wherein eachpredicted RPI corresponds to a different revenue model.

Further, in additional embodiments, a particular media having aparticular revenue model may be associated with a parcel of advertisingspace inventory that includes multiple individual tracts. In suchembodiments, the particular media may be associated with multiple targetmedia cells that collectively form the parcel of advertising spaceinventory. As such, the processes of FIG. 1 can predict a tract-levelRPI for each of the multiple target media cells associated with theparticular media and revenue model, and as described below in referenceto FIG. 6, combine these multiple tract-level RPI predictions into aparcel-level prediction for the RPI of the media and revenue model.

FIG. 2 illustrates an exemplary method 200 for selecting media cells,according to an embodiment of the present invention. For example, method200 may be incorporated into step 102 of FIG. 1 to select media cellsthat share one or more common attributes with a target media cell.

Step 202 identifies a tract, a revenue model, and a leadback model thatcharacterize a target media cell, such as the target media celldescribed above with reference to step 102 of FIG. 1. In an embodiment,the tract of the target media cell may include a website associated withthe target media cell, a slot size of the target media cell, and/or asegmentation model associated with the target media cell. In such anembodiment, the tract can define a “website-slot-segment” associatedwith the target media cell.

Further, in an embodiment, the segmentation model can include, but isnot limited to, frequency segmentation, a segmentation that definescookied and cookieless segments, and a geographic segmentation (e.g.,one that includes separate segments for the US, Canada, UK, and the restof world). In a further embodiment, any additional or alternatesegmentation model can characterize the target media cell withoutdeparting from the spirit or scope of the present invention.

Further, in an embodiment, the identified revenue model may include aclick-to-conversion (C2C) model, an impression-to-conversion (I2C)model, and/or a cost-per-click (CPC) model. For example, the C2C modelrefers to a campaign in which a user must click on a media served by anadvertising network and then complete some action before the advertisingnetwork receives payment from a publisher of the media. In contrast, theI2C model refers to a campaign in which the advertising network receivespayment when the user completes an action after seeing an impression ofthe media served by the advertising network, regardless of whether ornot that user clicked on the media. Further, the CPC model refers to acampaign in which the media server receives payment from a publisher ofa media when the end user clicks on the media. In further embodiments,any additional or alternate revenue model can characterize the targetmedia cell without departing from the spirit or scope of the presentinvention.

Further, in an embodiment, the target media cell may be a non-leadbackcell, or alternatively, the target media cell may be associated with anaudience leadback model or an advertiser leadback model. For example,the audience leadback model refers to a type of targeting that shows amedia to individuals who have previously visited some website ofinterest to a publisher of the media, other than the publisher's ownwebsite. Further, for example, the advertiser leadback model refers to atype of targeting that shows a media to individuals who have previouslyvisited the publisher's website. However, the target media cell is notlimited to such leadback models, and in further embodiments, anyadditional or alternative leadback model can characterize the targetmedia cell without departing from the spirit or scope of the presentinvention.

Once step 202 identifies the attributes of the target media cell, step204 identifies one or more media cells, which may or may not include thetarget media cell, and which share a common revenue model and a commontract definition with the target media cell. Step 206 filters theidentified media cells to separate non-leadback media cells from eachvariety of leadback media cells (e.g., advertiser-leadback media cellsand audience-leadback media cells).

Step 208 then processes the filtered non-leadback media cells to removeoutliers from the filtered set of media cells. Outliers may be mediacells whose estimated performance is either too high, or alternatively,too low, to be included in the RPI distribution modeling.

In an embodiment, step 208 removes outliers by first defining a minimumthreshold revenue per thousand impressions (RPM), RPM_(MIN), and amaximum threshold RPM, RPM_(MAX), for each tract and potentially, foreach revenue model, identified in step 202. Thresholds RPM_(MIN) andRPM_(MAX) are tunable parameters that, for example, can be setrespectively to $0.001 and $50 for media cells having I2C and C2Crevenue models.

Step 208 then removes a media cell from the set of filtered media cellsbased on a threshold certainty that the RPI of the media cell fallsoutside of the range [RPM_(MIN), RPM_(MAX)]. For example, step 208 canremove outliers based on a threshold certainty of 90%, i.e., a 90% orgreater certainty that the RPI of the media cell falls outside of therange [RPM_(MIN), RPM_(MAX)]. However, in additional embodiments, step208 can remove outlier cells based on any alternate threshold certaintyappropriate to the filtered media cells without departing from thespirit or scope of the invention.

To illustrate the removal of outlier cells in this embodiment, a mediamay have a cost-per-unit (CPU) of $1 and may have received 100,000impressions on a certain tract without receiving an action. While anobserved RPI for the media cell is zero, that cell is not classified asan outlier. Since the cell has received relatively few impressions, onlya small certainty exists that the RPM of the media cell is less than$0.001. In such an example, the media cell would have to be awardedapproximately 2.2 million impressions without receiving a single actionbefore sufficient certainty (e.g., a 90% certainty) exists that the RPMis less than $0.001.

Further, step 208 also processes the filtered non-leadback media cellsto remove those cells that are priced in a non-competitive fashion. Inan embodiment, media of a particular cell may be associated with acampaign that is priced below a market price of similar campaigns. Forexample, an advertising network may offer media, for example, “housemedia,” to its parent corporation at a discount to a prevailing marketprice. Such non-competitively priced media may be characterized by lowperformance and as such, may not be suitable for RPI distributionmodeling. In an embodiment, non-competitively priced media can beidentified in step 202 and can be removed in step 208 based on thisidentification.

Once the filtered media cells have been processed in step 208 to removeoutliers and/or house media, step 210 determines whether the targetmedia cell is associated with a particular leadback model. If step 210determines that the target media cell is a non-leadback media cell, thenthe processed media cells are output in step 212, after which the meanRPI of the processed cells may be estimated in step 104 of FIG. 1.

However, if step 210 determines that the target cell is associated witha particular leadback model, e.g., an audience leadback model or anadvertiser leadback model, then step 214 identifies media cells thatshare a common leadback model, a common revenue model, and/or a commontract definition with the target media cell. In an embodiment, step 214can also process these identified cells to remove both house ads andoutliers. Step 216 outputs the processed non-leadback media cells, asgenerated in step 208, and the identified set of leadback media cells,as identified in step 214, after which the mean RPI of the processednon-leadback cells may be estimated in step 104 of FIG. 1 andsubsequently adjusted for the identified leadback model.

FIG. 3 illustrates a method 300 for estimating a mean revenue perimpression (RPI) for a set of media cells using RPI distributionmodeling, according to an embodiment of the present invention. Forexample, method 300 can be incorporated into step 104 of FIG. 1 toestimate the mean RPI of the selected media cells.

Step 302 computes an error approximation for a mean RPI of a set ofselected media cells, such as those identified by the exemplary methodof FIG. 2. In an embodiment, the computed error approximation determineswhether, for the selected media cells, sufficient data exists to proceedwith RPI distribution modeling. A mean cell RPI estimate may be mostreliable when it is based on a large number of impressions from avariety of medias. Increasing both the number of medias used in thecalculation and the number of impressions each media has received maylead to a better estimate of the mean RPI for the selected cells.

In an embodiment, the error approximation K computed in step 302represents a ratio of a standard error of an estimate of mean cell RPIto an average cell RPI, as follows:

$\begin{matrix}{{K = {\frac{{standard}\mspace{14mu}{error}\mspace{14mu}{of}\mspace{14mu} R\; P\; I}{R\; P\; I} \approx \frac{1}{\sqrt{\sum\limits_{i}\frac{n_{i}}{n_{i} + {c_{i}/\mu_{N}}}}}}},} & (3)\end{matrix}$where n_(i) and c_(i) represent, respectively, a number of impressionsand a cost per unit for each media i in the set of selected media cells,μ_(N) is a tunable parameter that represents the network average RPI,and K ranges from zero to one. In various embodiments, μ_(N) depends ona particular revenue model of the selected media cells and a geographicsegmentation of the selected media cells, as the value of μ_(N) iscurrency-dependent.

Step 304 compares the error approximation computed in step 302 to athreshold parameter K_(T) to determine whether sufficient data exists toproceed with RPI distribution modeling. In an embodiment, data on theselected set of media cells can include, but is not limited to,information on a number of impressions gathered by the selected mediacells and a corresponding number of actions received by the selectedmedia cells.

For example, step 304 can determine whether K>K_(T). In an embodiment, aspecific value of K_(T) may reflect, for example, an estimate of aquality of the data on the selected set of media cells. Further, in anembodiment, the specific value of K_(T) can range from zero (indicatinglittle confidence in the quality of the data) to one (indicatingsubstantial confidence in the quality of the data).

In an embodiment, the threshold parameter K_(T) can be fixed at aparticular value for any revenue model or geographic segmentation of aselected set of media cells. However, in additional embodiments, thethreshold parameter K_(T) can be a tunable parameter that is variable inresponse to varying geographic segmentations, revenue models, or otherattributes. For example, a set of media cells on a given tract could beassigned a first threshold parameter for a first revenue model, whilethe same set of media cells having a different revenue model can beassigned a different threshold value.

If step 304 determines that the error approximation K is less than thethreshold parameter, K_(T), then sufficient information on the selectedmedia cells exists to estimate the mean RPI of the selected media cellsusing RPI distribution modeling. In such an instance, step 306calculates a distribution of RPI for the selected media cells. In anembodiment, the calculation of the distribution of RPI for the selectedmedia cells in step 306 includes at least: (i) a functional form of theprobability distribution of the RPI of the selected media cells; and(ii) a probability relationship between an RPI of a media within theselected media cells and a number of events that result from some givennumber of impressions.

For example, in certain embodiments, step 306 models a probability thata media has an RPI of r using a Gamma distribution family parameterizedby (t, λ), as follows:

$\begin{matrix}{{f(r)} = {\frac{{{\lambda\mathbb{e}}^{{- \lambda}\; r}\left( {\lambda\; r} \right)}^{t - 1}}{\Gamma(t)}.}} & (4)\end{matrix}$The Gamma distribution of Equation 4 describes a family of distributioncurves, where each distribution curve corresponds to a particular tractof advertising space inventory. In Equation 4, λ represents a “scalingfactor” that describes a “stretching” of each distribution curve, and trepresents a “shaping factor” that determines an existence or sharpnessof a peak of each distribution curve.

FIG. 4 is a logarithmic plot of the exemplary Gamma distribution ofEquation (4) for two different tracts of advertising space inventory.One tract, depicted by distribution curve 402, has an estimated mean RPMof $1.60, while the second tract, depicted by distribution curve 404,has an estimated mean RPM of 8.50. In FIG. 4, the respective mean RPMsof distribution curves 402 and 404 roughly correspond to the location ofthe peaks of the respective curves. In the log domain, λ affects alocation of the peak along the x-axis, while t affects a sharpness ofthe peak relative to its width.

Referring back to FIG. 3, step 306 may determine that a conditionedprobability for a media i with RPI n to receive a₁ events if it hasreceived n_(i) impressions is:

$\begin{matrix}\begin{matrix}{{{Prob}\left( {\left( {n_{l},a_{l}} \right)❘r_{l}} \right)} = {\begin{pmatrix}n_{i} \\a_{i}\end{pmatrix}\left( \frac{r_{i}}{c_{i}} \right)^{a_{i}}\left( {1 - \frac{r_{i}}{c_{i}}} \right)^{n_{i} - a_{i}}}} \\{\approx {\begin{pmatrix}n_{i} \\a_{i}\end{pmatrix}\left( \frac{r_{i}}{c_{i}} \right)^{a_{i}}{{\mathbb{e}}^{{- \frac{r_{i}}{c_{i}}}{({n_{i} - a_{i}})}}.}}}\end{matrix} & (5)\end{matrix}$The approximation of Equation 5 is based on an assumption that aconversion or click is a rare event, e.g., that a probability of gettingclicks or conversions is less than about 5%. However, the calculation instep 306 is not limited to such conditioned probabilities, and in analternate embodiment, the calculations of step 306 may use any alternateprobability relationship without departing from the spirit or scope ofthe present invention.

Based on the probability distribution of Equation 4 and the conditionedprobability of Equation 5, step 306 calculates the distribution ofrevenue per impression for the set of selected media cells. In such anembodiment, inputs to the calculation of step 306 may include: (i) a setof costs-per-unit (CPUs) c_(i) for the selected media cells and (ii) anumber of impressions n_(i) and number of events a_(i) for the set ofselected media cells.

Once the distribution has been calculated, step 306 uses a maximumlikelihood approach to determine parameters λ and t from the computedprobability distribution, as follows:

$\begin{matrix}\begin{matrix}{{L\left( {t,\lambda} \right)} = {\sum\limits_{i}{\int_{0}^{\infty}{{{prob}\left( {\left( {n_{i},a_{i}} \right)❘r_{i}} \right)}{f\left( r_{i} \right)}{\mathbb{d}r_{i}}}}}} \\{{= {\sum\limits_{i}{\int_{0}^{\infty}{\begin{pmatrix}n_{i} \\a_{i}\end{pmatrix}\left( \frac{r_{i}}{c_{i}} \right)^{a_{i}}{\mathbb{e}}^{{- \frac{n}{c_{i}}}{({n_{i} - a_{i}})}}\frac{{{\lambda\mathbb{e}}^{{- \lambda}\; r_{i}}\left( {\lambda\; r_{i}} \right)}^{t - 1}}{\Gamma(t)}{\mathbb{d}r_{i}}}}}},}\end{matrix} & (6)\end{matrix}$where L(t,λ) is a likelihood function. Using the Gamma integral formula,a likelihood function L(t,λ) takes the following form:

$\begin{matrix}{{L\left( {t,\lambda} \right)} = {\sum\limits_{i}{\frac{{\Gamma\left( {a_{i} + t} \right)}\lambda^{t}}{{\Gamma(t)}\left( {\lambda + \frac{n_{i}a_{i}}{c_{i}}} \right)^{a_{i} + i}}.}}} & (7)\end{matrix}$The likelihood function of Equation (7) can then be maximized usingexisting optimization tools to find an optimal t and λ.

Step 308 then computes a mean RPI for the set of selected media cellsbased on the probability distribution computed in step 306. In anembodiment, the mean of the distribution, which is the estimated meanRPI of the selected media cells, then takes the following form:

$\begin{matrix}{\mu = {\frac{t}{\lambda}.}} & (8)\end{matrix}$Furthermore, the variance of the estimated mean RPI for the selected setof media cells becomes:

$\begin{matrix}{{{var}(\mu)} = {\sigma_{\mu}^{2} = {\frac{t}{\lambda^{2}}.}}} & (9)\end{matrix}$Referring back to step 304, if the error approximation computed in step302 exceeds the threshold value (i.e., K>K_(T)), then the selected mediacells have gathered an insufficient number of impressions andcorresponding actions to accurately model the estimated mean RPI for theselected cells using RPI distribution modeling. In such an instance,step 310 computes a mean RPI for the selected media cells based on arelationship between attributes of one or more additional media cells(or sets of media cells) and estimated RPIs of the one or moreadditional media cells (or sets of media cells), which have beencomputed, respectively, from RPI distribution modeling.

In an embodiment, step 310 generates a model that predicts the estimatedmean RPI for each of the additional media cells (or sets of cells) basedon one or more attributes of the additional media cells (or sets ofcells), including, but not limited to, tract attributes such as website,slot size, and audience segmentation. The generated model then predictsa mean RPI for the selected media cells based on a correlation betweenone or more attributes of the selected media cells and correspondingattributes of the additional media cells (or sets of cells).

Once the mean RPI for the selected media cells has been computed, e.g.,through step 308 or step 310, step 312 tests whether the target mediacell is a non-leadback media cell. If the target media cell is anon-leadback media cell, step 314 outputs the computed mean RPI for theselected media cells, after which the RPI for the target media cell maybe predicted by step 106 of FIG. 1.

However, if step 312 determines that the target media cell is a leadbackcell, then step 316 adjusts the computed mean RPI for the selected mediacells to account for the leadback model of the target cell.

Leadback medias are medias that are targeted at individuals withspecific web-browsing history. In certain embodiments, leadback mediasmay exhibit higher RPIs than non-leadback medias. Such behavior is anexample of an attribute effect, as described above. Leadback mayinclude, for example, audience leadback and advertiser leadback.

Audience leadback targets individuals who have visited certain contentsites in an advertising network. For example, medias advertising a newvehicle may be targeted at individuals who have visited automobilereview sites. Advertiser leadback targets individuals who havepreviously visited the advertiser's specific site. For example,customers who have previously shopped at an on-line retailer may beshown ads or offered special coupons from that same retailer. In certainembodiments, leadback models use cookies stored on a consumer's computerto recognize that the consumer has previously visited the website andthus meets the targeting criteria.

In an embodiment, step 316 models the effect of the leadback model, suchas advertiser leadback or audience leadback, by applying amultiplicative factor to the mean RPI of the selected media cells oftract j, μ_(j). For example, historical data can be used to derivestatistical properties of a factor h, which relates a mean RPI of aleadback media to a mean RPI of a corresponding non-leadback media. Inparticular, a mean of factor h (denoted by h) can be derived and canthen be used to scale the mean RPI of the selected media cells, μ_(j),to obtain an initial estimate for leadback media on segment j.

In an embodiment, step 316 estimates mean of factor h, h, by firstassuming a functional form for a distribution of h. For example, step316 can model h using a Gamma distribution family parameterized by (t,λ), as follows:

$\begin{matrix}{{f(h)} = {\frac{{{\lambda\mathbb{e}}^{{- \lambda}\; h}\left( {\lambda\; h} \right)}^{t - 1}}{\Gamma(t)}.}} & (10)\end{matrix}$As described above in reference to the assumed distribution for RPI instep 316, λ is a scaling factor that describes a stretching of adistribution curve, and t is a shaping factor that determines anexistence or sharpness of a peak of a distribution curve.

Conditional on h, a probability of observing n_(ij) impressions anda_(ij) actions for media i with cost per unit (CPU) c_(i) on tract jwith tract mean RPI μ_(j) is modeled as:

$\begin{matrix}{{{Prob}\left( {\left( {n_{ij},a_{ij}} \right)❘h} \right)} = {\frac{h\;\mu_{j}{{\mathbb{e}}^{{- h}\;\mu\;{{jn}_{ij}/c_{i}}}\left( {h\;\mu_{j}{n_{ij}/c_{i}}} \right)}^{{a_{ij}/c_{i}} - 1}}{c_{i}{\Gamma\left( {a_{ij}/c_{i}} \right)}}.}} & (11)\end{matrix}$

As such, the overall likelihood L of observing (n_(ij), a_(ij)) is:

$\begin{matrix}\begin{matrix}{{L\left( {t,\lambda} \right)} = {\int_{0}^{\infty}{{{Prob}\left( {\left( {n_{ij},a_{ij}} \right)❘h} \right)}{f(h)}{\mathbb{d}h}}}} \\{= {\frac{{\Gamma\left( {{a_{ij}/c_{i}} + t} \right)}\left( {n_{ij}/c_{i}} \right)^{{a_{ij}/c_{i}} - 1}\lambda_{h}^{t}\mu_{j}^{a_{ij}/c_{i}}}{c_{i}{\Gamma\left( {a_{ij}/c_{i}} \right)}{\Gamma(t)}\left( {\lambda + {\mu_{j}{n_{ij}/c_{i}}}} \right)^{{a_{ij}/c_{i}} + t}}.}}\end{matrix} & (12)\end{matrix}$

The above-described likelihood is valid for a media cell or set of mediacells that have gathered at least one action, i.e., a_(ij)≠0. For amedia cell or set of media cells that have no observed actions, i.e.,a_(ij)=0, step 316 considers a probability of no payouts in n_(ij)impressions given the payout rate hμ_(j). This event can alternativelybe described as the probability that the first conversion occurs laterthan n_(ij):

$\begin{matrix}{{{Prob}\left( {n_{ij},0} \right)} = {{\mathbb{e}}^{\frac{r_{ij}n_{ij}}{c_{i}}}.}} & (13)\end{matrix}$

Under this assumption:

$\begin{matrix}\begin{matrix}{{L\left( {t,\lambda} \right)} = {\int_{0}^{\infty}{{{Prob}\left( {\left( {n_{ij},a_{ij}} \right)❘h} \right)}{f(h)}{\mathbb{d}h}}}} \\{= {\frac{\lambda^{t}}{\left( {\lambda + {\mu_{j}{n_{ij}/c_{i}}}} \right)^{t}}.}}\end{matrix} & (14)\end{matrix}$

Step 316 then estimates parameters λ and t by maximizing the likelihoodfunction over all observations, i.e., through a maximum likelihoodapproach. Using t and λ, step 316 then computes

${\overset{\_}{h} = \frac{t}{\lambda}},$and an initial RPI estimate for a narrowly targeted media on tract j isthen:μ_(j) ^(T) = hμ _(j).  (15)

If μ_(j) ^(T) serves as the estimated mean RPI for selected media cells,then the variance of estimation error will be the variance of theestimated Gamma distribution, as follows:

$\begin{matrix}{\sigma_{\mu^{T}}^{2} = {\frac{t}{\lambda^{2}}{\mu_{j}^{2}.}}} & (16)\end{matrix}$

As such, in the presence of a leadback model associated with the targetcell, step 316 computes a product of the estimated mean RPI for theselected non-leadback media cells and the multiplicative factor h. Onceadjusted in step 316, the estimated, adjusted mean RPI for the selectedmedia cells is output by step 318, after which step 106 of FIG. 1 maypredict the mean RPI for the target media cell.

FIG. 5 depicts a process 500 for computing a mean RPI for a set of mediacells having insufficient impression data for RPI distribution modeling,according to an embodiment of the present invention. For example,process 500 may be incorporated into step 310 of FIG. 3 to compute themean RPI for the selected media cells when K>K_(T).

Step 502 constructs a relationship between estimates of mean RPIs foradditional media cells or sets of media cells, which have been computedfrom probabilistic distributions of RPI (e.g., in step 306 and 308 ofFIG. 3) and attributes of the various media cells or sets of mediacells. The attributes can include but are not limited to tractattributes, such as website, slot size, and behavior segment group.However, the processes described herein are not limited to tractattributes, and in additional embodiments, step 502 can construct arelationship between a mean RPI of a media cell or set of media cellsand any additional or alternate attribute without departing from thespirit or scope of the present invention.

TABLE 2 Website Slot Size User Segment Group RPI AOL 1 .EDU $1e-4 AOL 2.COM $5e-4 AOL 1 .COM $3e-4 Yahoo! 1 .COM $4e-4 . . . . . . . . . . . .

Table 2 illustrates exemplary estimates of mean RPI and correspondingvalues of tract attributes for several exemplary media cells (or sets ofmedia cells). In this embodiment, w_(i) ^(k) denotes the factorcorresponding to value i of attribute k. For example, using website asthe first attribute (i.e., k=1), slot size as the second attribute(i.e., k=2), and user segment group as the third attribute (i.e., k=3),Tables 3A-3C list an exemplary factor attribute correspondence:

TABLE 3A AOL Yahoo! AOL-Mail CNN . . . w₁ ¹ w₂ ¹ w₃ ¹ w₄ ¹ . . .

TABLE 3B Slot 1 Slot 2 Slot 3 Slot 4 . . . w₁ ² w₂ ² w₃ ² w₄ ² . . .

TABLE 3C .Edu .Com .Net 3 . . . w₁ ³ w₂ ³ w₃ ³ . . .

In this embodiment, b_(j) ^(k) denotes the index of the k^(th) attributeof segment j. For example, if segment 8, i.e. j=8, is “CNN,Slot2,.Edu”from Table 2, then b₈ ¹=4, b₈ ²=2, b₈ ³=1.

In this embodiment, step 502 assumes a logarithmic-linear relationshipbetween the factors (w_(i) ^(k)) associated with a particular media cellj (or set of media cells j) and the corresponding mean RPI (μ_(j)) forthe media cell (or set of media cells). In particular, for the threeattributes described above, step 502 assumes:log(μ_(j))=w _(b) _(j) ₁ ¹ +w _(b) _(j) ₂ ² +w _(b) _(j) ₃ ³,  (17)or, in general for any number of attributes:

$\begin{matrix}{{\log\left( \mu_{j} \right)} = {\sum\limits_{k}{w_{b_{j}^{k}}^{k}.}}} & (18)\end{matrix}$

The above-described model can be alternatively explained using thefollowing notations. Using a matrix for the k^(th) attribute, defined asD^(k)={d_(ij) ^(k)},

$\begin{matrix}{d_{ij}^{k} = \left\{ \begin{matrix}0 & {{{{if}\mspace{14mu} i} \neq b_{j}^{k}};} \\1 & {{{if}\mspace{14mu} i} = {b_{j}^{k}.}}\end{matrix} \right.} & (19)\end{matrix}$

Step 504 may set W^(k)=[w₁ ^(k) w₁ ^(k) w_(l) _(k) ^(k)], where l_(k) isthe number of distinct values for the k^(th) attribute. Now, ifD:=[D^(l) D² . . . ], W:=[W¹ W² . . . ], and η=[log(Φ₁) log(Φ₂) . . . ],the regression can be expressed by step 502 as:η=DW.  (20)

In an embodiment, step 504 can solve the regression of Equation (20) forW using a least squares (LS) approach, thereby obtaining the set offactors w_(i) ^(k) that describe the relationship between the attributesof media cell j (or set of media cells)) and the mean RPI of media cellj (or set of media cells).

Once step 504 determines factors for the additional media cells or setof media cells having probabilistically-computed estimates of mean RPI,step 506 then estimates the mean RPI for the selected media cells basedon a correlation between attributes of the selected media cells and thecomputed factors w_(i) ^(k).

When estimating the mean RPI for the selected media cells, such as thoseidentified in FIG. 2, step 506 may determine, for example, that:

-   -   (i) all factors w_(i) ^(k) that describe the attributes of the        selected media cells are available without aliasing;    -   (ii) all factors w_(i) ^(k) that describe the attributes of the        selected media cells are available, but aliasing exists; or    -   (iii) some factors w_(i) ^(k) that describe the attributes of        the selected media cells are not available.

In scenario (i), step 504 has computed factors corresponding to threeattributes (e.g., website, slot size, and segmentation model) thatdescribe the selected media cells. As such, step 506 can estimate themean revenue per impression for the selected media cells, μ_(cells), as:log(μ_(cells))=w _(b) _(cells) ₁ ¹ +w _(b) _(cells) ₂ ² +w _(b) _(cells)₃ ³,  (21)or, for any arbitrary number of attributes K, as:

$\begin{matrix}{{\log\left( \mu_{cells} \right)} = {\sum\limits_{k = 1}^{K}{w_{b_{cells}^{k}}^{k}.}}} & (22)\end{matrix}$In the above equations, b_(cells) ^(k), denotes the index of the k^(th)attribute of the selected media cells, and w_(b) _(cells) _(k) ^(k)denotes the factor computed in step 502 that corresponds to indexb_(cells) ^(k).

The variance of the estimate of the mean RPI computed by step 506 can beexpressed as:var(μ_(cells))=σ_(μ) ²=βμ²,  (23)where β is a tunable parameter and empirically chosen to provide a bestfit to the data. In an embodiment, the chosen value β lies in a rangefrom one to five. However, in additional embodiments, the value of β mayfall above or below this exemplary range without departing from thespirit or scope of the present invention. Further, in an additionalembodiment, β can be initially set to unity and periodically reviewedand adjusted, for example, in an effort to achieve better fit as theselected media cells gather more impressions and actions.

However, in situation (iii), one or more factors may not exist or maynot be combined using Equations 21 and 22. For example, in a set ofselected media cells characterized by website A, slot B, and a usersegment group C, if a factor corresponding to website A is notavailable, step 506 can replace this unknown factor by an average factorderived from all other available website factors associated with slot Band user segment group C. Once this average factor is derived, the meanrevenue per impression for the selected media cells can be estimated asin scenario (i). The following example, summarized in Table 4,illustrates the operation of steps 502, 504, and 506 in view ofscenarios (i) and (iii) described above.

In this exemplary embodiment, nine non-leadback media cells (oralternatively, sets of media cells) of a specific revenue model havebeen characterized in terms of three tract attributes: a website, aslot, and a segmentation model. In the example of Table 4, a meanrevenue per thousand impressions (RPM) may have been estimated for cells1-7 (or sets of media cells 1-7) using RPI distribution modeling, e.g.,as described above in reference to steps 306 and 308 of FIG. 3.

TABLE 4 Row # Website Slot Segmentation μ × 1000 1 CoolPortal 10Frequency 1  $1.30 2 CoolPortal 10 Frequency 5-9 $0.20 3 CoolPortal 21Frequency 1  $1.75 4 CoolPortal 21 Frequency 5-9 $0.25 5 Mybook 10Frequency 1  $0.40 6 Mybook 10 Frequency 5-9 $0.05 7 Mybook 21 Frequency1  $0.60 8 Mybook 21 Frequency 5-9 ? 9 BittyBlog 21 Frequency 1  ?

Rows 8 and 9 of Table 4 describe respective media cells (or respectivesets of media cells) that lack sufficient impression data to compute amean RPI using RPI distribution modeling. As such, the mean revenue perimpression for these cells or sets of cells is unknown. The followingexample illustrates the estimation of these mean RPIs, i.e., μ₈ and μ₉,using the processes of FIG. 5.

As described above in reference to step 502, the mean RPI for each ofthe media cells or sets of media cells in Rows 1-7 of Table 4 candetermined from factors w_(website), w_(slot), and w_(segmentation) asfollows:log(μ)=w _(website) +w _(slot) +w _(segmentation).  (24)

Thus, in the embodiment of Table 4:

$\begin{matrix}{{{\log\left( \mu_{1} \right)} = {w_{CoolPortal} + w_{{slot}\; 10} + w_{{freq}\; 1}}}{{\log\left( \mu_{2} \right)} = {w_{CoolPortal} + w_{{slot}\; 10} + w_{{{freq}\; 5} - 9}}}{{\log\left( \mu_{3} \right)} = {w_{CoolPortal} + w_{{slot}\; 21} + w_{{freq}\; 1}}}\mspace{160mu}\vdots{{\log\left( \mu_{6} \right)} = {w_{Mybook} + w_{{slot}\; 10} + w_{{{freq}\; 5} - 9}}}{{{\log\left( \mu_{7} \right)} = {w_{Mybook} + w_{{slot}\; 21} + w_{{freq}\; 1}}},}} & (25)\end{matrix}$where subscripts applied to each μ refer to the row numbers in Table 4.In this embodiment, each mean RPI, μ, for Rows 1-7 has been computedthrough RPI distribution modeling, as described above in steps 306 and308 of FIG. 3.

In this embodiment, step 504 computes the factors w_(website), w_(slot)and w_(segmentation) for media cells 1-7 (or sets of media cells 1-7) inTable 4 using a least-squares approach. Once the individual factorsw_(website), w_(slot), and w_(segmentation) have been calculated, step506 estimates the mean RPI for media cell 8 (or set of media cells 8)as:log(μ₈)=w _(Mybook) +w _(slot21) +w _(freq5-9).  (26)

Furthermore, step 506 estimates the mean RPI for media cell 9 (or set ofmedia cells 9) of Table 4 as:log(μ₉)=w _(BittyBlog) +w _(slot21) +w _(freq1).  (27)

However, no media cell having a previously-estimated mean RPI ischaracterized by the “BittyBlog” website. As such, as described abovefor situation (iii), step 506 estimates w_(BittyBlog) by averaging overthe values of w_(website) that have been computed by step 504. In thesimplified example of Table 4, step 506 would average the values ofw_(CoolPortal) and w_(Mybook) computed in step 504.

In other embodiments, step 504 can compute factors corresponding tohundreds of individual websites associated with media cells or sets ofmedia cells having common revenue models and, potentially, commongeographic segmentations. In such a case, the averaging process of step506 could include factors associated with hundreds of websites. Further,although not described in the embodiment of Table 4, the averagingprocess of scenario (iii) of step 506 could determine any other unknownfactor or plurality of factors associated with a corresponding attributeof the selected media cells, including, but not limited to, the slot andsegmentation attributes of Table 4.

Further, the embodiment of Table 4 includes only two segment definitionsfor each media cell or set of cells. However, in additional embodiments,the processes of FIG. 5 can include any additional definition from thatsegment set, e.g., Frequency 2-4 and Frequency 10-19, or definitionsfrom any additional or alternate segmentation schemes without departingfrom the spirit or scope of the present invention.

Additionally, method 500 is not limited to characterizations of mediacells according to three tract-based attributes, as defined above. Inadditional embodiments, process 500 can be generalized to consider anynumber of attributes apparent to one skilled in the art and relevant toa specific application.

Referring back to FIG. 5, in certain embodiments, when all factors wkthat describe the attributes of the selected media cells may have beencomputed in the presence of aliasing (i.e., scenario (ii) describedabove). Aliasing occurs when the regression solution is not unique.Therefore, there exists one or more sets of parameters that, once theregression is computed in step 504, produce the same resulting set offactors. These estimated parameters produce meaningful predictions onlyin cases that all the family members generate the same result.

In certain embodiments, aliasing will be present when the design matrixD in Equation 20 is not full column rank, i.e., design matrix D has anull space N_(D). As such, anything from null space N_(D) can be addedto W without any impact on the model in Equation 20. Therefore, thefactor estimates that obtained from the regression in step 504 are notunique, i.e., W=W+ν, where ν is any arbitrary vector from N_(D).

In an embodiment, the prediction of factors for a media or set of mediason a tract of advertising space inventory can be generated by firstforming a design row d_(p) that corresponds to the tract, and then byapplying η_(p)=d_(p)(μ₀+ν), where μ₀ is a mean RPI for the media or setof medias on the tract. In this embodiment, the resulting predictionη_(p) is meaningful only if it is unique. In other words, arbitraryvector v does not have any impact on η_(p). Such a result may occur ifd_(p) is orthogonal to null space N_(D). Thus, for any tract whosedesign vector is not orthogonal to N_(D), step 504 may not be able topredict factors based on a logistic regression.

In such a case, if step 506 is unable to estimate the mean revenue perimpression for the selected media cells using a logarithmic-linearcombination of factors, step 506 can estimate the mean RPI of theselected media cells by averaging the estimated mean RPI for media cellsor sets of media cells that share a maximum number of common attributeswith the selected media cells.

FIG. 6 illustrates a method 600 for predicting a revenue per impression(RPI) for a target media through data sharing, according to anembodiment of the present invention. For example, method 600 can beincorporated into step 106 of FIG. 1 to predict a RPI for a target mediacell based on an estimated mean RPI for the selected media cells.

Step 602 obtains data on the historical performance of a target mediacell. In an embodiment, such data includes a number of impressionsreceived or gathered by the target media cell and a number ofcorresponding actions received by the target media cell or cells. Invarious embodiments, such data may be obtained directly throughcontinuous measurement and monitoring of activity associated with thetarget media cell. Furthermore, in an embodiment, the historical dataobtained in step 602 may refer to the performance of a target mediaacross multiple target media cells, i.e., across a parcel of advertisingspace inventory.

Step 604 defines an initial estimate of the RPI of the target media cellas the estimated mean RPI of the selected media cells. In such anembodiment, both the initial estimate of the RPI of the target mediacell and the estimated mean RPI for the selected media cells represent“tract-level” performance, as these estimates correspond to a specifictract of advertising space inventory, e.g., a particularwebsite-slot-segment of advertising space inventory.

In an additional embodiment, steps 602 and 604 can be repeated for eachtarget media cell associated with a particular target media. Forexample, a target media can be associated with multiple tracts ofadvertising space inventory, thereby defining multiple target mediacells. As such, step 602 can obtain historical data for each targetmedia cell, and step 604 could subsequently define an initial RPIestimate for each target media cell associated with the target media.

Step 606 rolls up the tract-level performance estimates for the targetmedia cell or cells into “parcel-level” performance estimates. Asdescribed above, the estimated mean RPI for the selected media cells,and hence the corresponding initial performance estimate for the targetmedia cell, may represent tract-level estimates. However, otherperformance measurements, including, but not limited to, historical dataon the performance of the target media cell of step 602, may be based onmeasurements and observations across multiple target media cells, e.g.,across a parcel of advertising space inventory. As such, beforecombining these performance metrics to predict the RPI for the targetmedia cell, the individual tract-level RPI predictions must be rolled-upto the parcel level.

In an embodiment, a parcel of advertising space inventory can include asingle tract of advertising space inventory, i.e., the parcel includes asingle target media cell. In such an instance, the tract-levelprediction of the initial RPI for the target media cell defined in step604 is already a parcel-level prediction, and no additional processingoccurs in step 606.

However, in an additional embodiment, a parcel can include a pluralityof individual tracts. In such an instance, the parcel may be formed frommultiple target media cells, each of which having a correspondinginitial RPI estimate defined according to step 604. In such a case, aweighted average of the individual tract predictions is used as theparcel prediction:

$\begin{matrix}{{{\hat{p}}_{ij}^{{data} - {sharing}} = \frac{\sum\limits_{s \in j}{{\hat{p}}_{is}^{{data} - {sharing}}n_{s}^{RTD}}}{\sum\limits_{s \in j}n_{s}^{RTD}}},} & (28)\end{matrix}$where {circumflex over (p)}_(ij) ^(data-sharing) is the parcel-levelpredicted RPI for media i on parcel j, while {circumflex over(p)}^(data-sharing) is the tract-level initial estimate of RPI for mediai on tract s within parcel j (i.e., the initial RPI for target mediacell s, defined above in step 604). n_(s) ^(RTD) is the number ofimpressions targeted at each target media cell over a time period, forexample, a two-week period.

The standard deviation of {circumflex over (p)}_(ij) ^(data-sharing) isrolled up from the tract-level standard deviations in the same manner:

$\begin{matrix}{{\sigma_{ij}^{{data} - {sharing}} = \frac{\sum\limits_{s \in j}{\sigma_{is}^{{data} - {sharing}}n_{s}^{RTD}}}{\sum\limits_{s \in j}n_{s}^{RTD}}},} & (29)\end{matrix}$where standard deviation and variance are related as:σ_(is) ^(data-sharing)=√{square root over (var({circumflex over (p)}_(is) ^(data-sharing)))}σ_(ij) ^(data-sharing)=√{square root over (var({circumflex over (p)}_(ij) ^(data-sharing)))}.  (30)

Once step 606 defines a parcel-level estimate of the initial RPI for thetarget media, step 608 predicts a parcel-level RPI of the target media.In an embodiment, step 608 blends the initial, parcel-level estimate ofthe RPI of the target media and the historical data of the performanceof the target media to compute the RPI of the target media.

These two contributions to the RPI for the target media are weighed andsummed to yield the final performance prediction:

$\begin{matrix}{{{\hat{p}}_{blended} = \frac{{w_{{data} - {sharing}} \times {\hat{p}}_{{data} - {sharing}}} + {w_{{cell} - {specific}} \times {\hat{p}}_{{cell} - {specific}}}}{w_{{data} - {sharing}} + w_{{cell} - {specific}}}},} & (31)\end{matrix}$where {circumflex over (p)}_(blended) represents the final RPI of thetarget media at the parcel level; {circumflex over (p)}_(data-sharing)represents the initial RPI of the target media at the parcel level, asobtained from Equation 28, above; and {circumflex over(p)}_(cell-specific) represents historical observed performance at thetarget cell at the parcel level. Further, w_(data-sharing) andw_(cell-specific) represent, respectively, weight factors associatedwith {circumflex over (p)}_(data-sharing) and w_(cell-specific).

In the embodiment of FIG. 6, the weight given to the initial RPI of thetarget media and the weight given to the historical observed performanceare, respectively, proportional to a variance associated with thecorresponding RPIs. For example, if the variance associated with theinitial RPI of the target media is larger than the variance associatedwith the historical observed performance, step 608 would consider theinitial revenue per impression of the target cell a less reliablepredictor of the final revenue per impression of the target cell.Accordingly, step 608 would weigh the initial revenue per impression ofthe target cell less heavily than the historical observed performancewhen computing the final revenue per impression for the target mediacell.

In an embodiment, a weight given to the data sharing contribution, i.e.,the initial RPI estimate for the target media, is:

$\begin{matrix}{{w_{{data} - {sharing}} = \frac{1}{c \times {\hat{p}}_{{data} - {sharing}}}},} & (32)\end{matrix}$with the tunable constant c currently set to unity. Furthermore, theweight given to the cell-specific contribution, i.e., the historicalobserved performance of the target media, is equal to thelag-compensated number of impressions at the cell:w _(cell-specific) =n _(lag-compensated).  (33)In an embodiment, the lag-compensated number of impressionsn_(lag-compensated) can be set equal to a number of impressions thathave so far been awarded to the target cell.

The following examples illustrate how the blending process of FIG. 6 maypredict the final RPI for the target cell. First, consider a casewherein a cell has not yet received even a single impression. At thattime:w _(cell-specific) =n _(lag-compensated)=0.  (34)

In this exemplary case, the final RPI for the target media cell, aspredicted in step 608, reduces to the initial RPI of the target mediacell predicted in step 606, as expected.

However, in another case, a target media cell receives impressions, butstill does not receive any actions. When no actions have been received,the cell-specific performance estimate {circumflex over(p)}_(cell-specific). Further, for exemplary purposes only, assume thatan initial RPI of the target media cell (i.e., the data-sharingprediction) is 0.0001, which indicates that an action is expected onaverage for every 10,000 impressions shown. FIG. 7 illustrates thebehavior of the prediction of the RPI for the target media cell, ascomputed in step 608, changes as the target cell gathers more and moreimpressions.

The behavior of the predicted mean RPI for the target media cell, asdepicted in FIG. 7, indicates that the initial estimate of mean RPI forthe target cell (i.e., the data sharing estimate) dominates thepredicted mean RPI while the number of impressions gathered by thetarget cell remains small. However, as the number of impressionsincreases towards 30,000, the predicted mean RPI for the target celldeclines, since the observed performance at the target cell (i.e., noaction) dominates the final revenue per impression. As such, since thetarget cell has not gathered a single action after a large number ofimpressions, the mean RPI for the target cell predicted by step 608indicates that the target cell is a poor performer.

Furthermore, as described above, the processes of FIG. 6 are not limitedto parcels that include multiple tract definitions. For a parcel thatincludes only a single tract, the parcel-level definition of the initialRPI for the target media, as computed in step 606, is equivalent to thepredicted initial estimate of the mean RPI for the target media cell, asthe target media cell coincides with the parcel. As such, the resultingRPI predicted by step 608 will correspond to the RPI of the target mediacell.

The underlying premise of data sharing is that similar cells will havesimilar performance, as measured by RPI. Thus, as outlined above inreference to FIGS. 6 and 7, observations of the performance of a groupof peer cells can be used to generate performance predictions for cellswith no history that substantially reduce or eliminate the biasassociated with conventional performance estimates. Furthermore, datasharing can be used to enhance the performance estimates for all cellsby blending cell-specific history with data from related cells, asdescribed in step 608.

4. Exemplary Computer Systems

FIG. 8 is an exemplary computer architecture 800 upon which the methodsand systems of the present invention may be implemented, according to anembodiment of the invention. Exemplary computer system 800 includes oneor more processors, such as processor 802. Processor 802 is connected toa communication infrastructure 806, such as a bus or network.

Computer system 800 also includes a main memory 808, for example, randomaccess memory (RAM), and may include a secondary memory 810. Thesecondary memory 810 may include, for example, a hard disk drive 812and/or a removable storage drive 814, representing a magnetic tapedrive, an optical disk drive, CD/DVD drive, etc. The removable storagedrive 814 reads from and/or writes to a removable storage unit 818 in awell-known manner. Removable storage unit 818 represents a magnetictape, optical disk, or other storage medium that is read by and writtento by removable storage drive 814. As will be appreciated, the removablestorage unit 818 can represent a computer readable medium having storedtherein computer programs, sets of instructions, code, or data.

In alternative implementations, secondary memory 810 may include othermeans for allowing computer programs or other program instructions to beloaded into computer system 800. Such means may include, for example, aremovable storage unit 822 and an interface 820. An example of suchmeans may include a removable memory chip (e.g., EPROM, RAM, ROM, DRAM,EEPROM, flash memory devices, or other volatile or non-volatile memorydevices) and associated socket, or other removable storage units 822 andinterfaces 820, which allow instructions and data to be transferred fromthe removable storage unit 822 to computer system 800.

Computer system 800 may also include one or more communicationsinterfaces, such as communications interface 824. Communicationsinterface 824 allows software and data to be transferred betweencomputer system 800 and external devices. Examples of communicationsinterface 824 may include a modem, a network interface (e.g., anEthernet card), a communications port, a PCMCIA slot and card, etc.Software and data may be transferred via communications interface 824 inthe form of signals 826, which may be electronic, electromagnetic,optical or other signals capable of being received by communicationsinterface 824. These signals 826 are provided to communicationsinterface 824 via a communications path (i.e., channel) 828. Thischannel 828 carries signals 826 and may be implemented using wire orcable, fiber optics, an RF link and other communications channels. In anembodiment of the invention, signals 826 comprise data packets sent toprocessor 802. Information representing processed packets can also besent in the form of signals 826 from processor 802 throughcommunications path 828.

The terms “storage device” and “storage medium” may refer to particulardevices including, but not limited to, main memory 808, secondary memory810, a hard disk installed in hard disk drive 812, and removable storageunits 818 and 822. Further, the term “computer readable medium” mayrefer to devices including, but not limited to, a hard disk installed inhard disk drive 812, any combination of main memory 808 and secondarymemory 810, and removable storage units 818 and 822, which respectivelyprovide computer programs and/or sets of instructions to processor 802of computer system 800. Such computer programs and sets of instructionscan be stored within one or more computer readable mediums. Additionallyor alternatively, computer programs and sets of instructions may also bereceived via communications interface 824 and stored one or morecomputer readable mediums.

Such computer programs and instructions, when executed by processor 802,enable processor 802 to perform the computer-implemented methodsdescribed above. Examples of program instructions include, for example,machine code, such as produced by a compiler, and files containing ahigh-level code that can be executed by processor 802 using aninterpreter.

Furthermore, the computer-implemented methods described above inreference to FIGS. 1-7 can be implemented on a single processor of acomputer system, such as processor 802 of system 800. However, in anadditional embodiment, the computer-implemented methods of FIGS. 1-7 maybe implemented using one or more processors, such as processor 802,within a single computer system, and additionally or alternatively,these computer-implemented methods may be implemented on one or moreprocessors within separate computer systems linked via a network.

In the preceding specification, various embodiments have been describedwith reference to the accompanying drawings. It will, however, beevident that various modifications and changes may be made thereto, andadditional embodiments may be implemented, without departing from thebroader scope of the invention as set forth in the claims that follow.

Further, other embodiments of the present invention will be apparent tothose skilled in the art from consideration of the specification andpractice of one or more embodiments of the invention disclosed herein.It is intended that the specification and examples be considered asexemplary only, with a true scope and spirit of the invention beingindicated by the following claims.

What is claimed is:
 1. A computer-implemented method, comprising:generating an approximation to an error associated with a mean revenueper impression of a corresponding media cell, the corresponding mediacell sharing one or more common attributes with a target media cell, andthe error approximation being based on at least a number of impressionsassociated with the corresponding media cell; determining, with at leastone processor, whether the error approximation exceeds a threshold valueassociated with a revenue model of the corresponding media cell;calculating, when the error approximation does not exceed the thresholdvalue, the mean revenue per impression of the corresponding media cellbased on a distribution of revenue per impression associated with thecorresponding media cell; and predicting, with the at least oneprocessor, a revenue per impression of the target media cell based onthe calculated mean revenue per impression of the corresponding mediacell.
 2. The method of claim 1, wherein the common attributes compriseat least one of a common tract of advertising space inventory, a commonrevenue model, a common slot size, a common segmentation model, a commonmedia, or a common industry campaign.
 3. The method of claim 1, furthercomprising: identifying a plurality of media cells that share the one ormore common attributes with the target media cell; and computing anapproximation to an error associated with a mean revenue per impressionof the identified media cells, based on at least a number of impressionsassociated with the identified media cells.
 4. The method of claim 1,wherein the generating comprises: calculating a factor indicative of arevenue model of the corresponding media cell and a geographicsegmentation of the corresponding media cell; and computing the errorapproximation based on at least one of the number of impressionsassociated with the corresponding media cell or a ratio of (i) a costper unit of media associated with the corresponding media cell and (ii)the calculated factor.
 5. The method of claim 1, wherein the calculatingcomprises determining the distribution of revenue per impression for thecorresponding media cell based on at least one of a cost per unit ofmedia associated with the corresponding media cell, the number ofimpressions associated with the corresponding media cell, or a number ofevents associated with the corresponding media cell.
 6. The method ofclaim 1, further comprising: when the error approximation exceeds thethreshold value, calculating the mean revenue per impression of thecorresponding media cell based on a relationship between a plurality ofattributes of one or more additional media cells and an estimated meanrevenue per impression of the one or more additional media cells.
 7. Themethod of claim 6, wherein the calculating further comprises:determining a plurality of factors that describe a relationship betweenthe attributes of the one or more additional media cells and theestimated mean revenue per impression of the one or more additionalmedia cells, wherein each of the plurality of factors is associated witha corresponding one of the plurality of attributes; and calculating themean revenue per impression of the corresponding media cell based on alogarithmic-linear combination of the plurality of factors.
 8. Themethod of claim 6, wherein the plurality of attributes comprise at leastone of a website, a slot size, or a segmentation model associated witheach additional media cell.
 9. The method of claim 1, wherein thepredicting comprises computing a weighted average of (i) the estimatedmean revenue per impression of the corresponding media cell and (ii)measurements of revenue per impression for the target media cell. 10.The method of claim 1, wherein the calculating comprises adjusting themean revenue per impression of the corresponding media cell to accountfor one or more of audience leadback and advertiser leadback.
 11. Anapparatus, comprising: a storage device; and a processor coupled to thestorage device, wherein the storage device stores a program forcontrolling the processor, and wherein the processor, being operativewith the program, is configured to: generate an approximation to anerror associated with a mean revenue per impression of a correspondingmedia cell, the corresponding media cell sharing one or more commonattributes with a target media cell, and the error approximation beingbased on at least a number of impressions associated with thecorresponding media cell; determine whether the error approximationexceeds a threshold value associated with a revenue model of thecorresponding media cell; calculate, when the error approximation doesnot exceed the threshold value, the mean revenue per impression of thecorresponding media cell based on a distribution of revenue perimpression associated with the corresponding media cell; and predict arevenue per impression of the target media cell based on the calculatedmean revenue per impression of the corresponding media cell.
 12. Theapparatus of claim 11, wherein the common attributes comprise at leastone of a common tract of advertising space inventory, a common revenuemodel, a common slot size, a common segmentation model, a common media,or a common industry campaign.
 13. The apparatus of claim 11, whereinthe processor is further configured to: calculate a factor indicative ofa revenue model of the corresponding media cell and a geographicsegmentation of the corresponding media cell; and compute the errorapproximation based on at least one of the number of impressionsassociated with the corresponding media cell or a ratio of (i) a costper unit of media associated with the corresponding media cell and (ii)the calculated factor.
 14. The apparatus of claim 11, wherein theprocessor is further configured to determine the distribution of revenueper impression for the corresponding media cell based on at least one ofa cost per unit of media associated with the corresponding media cell,the number of impressions associated with the corresponding media cell,or a number of events associated with the corresponding media cell. 15.The apparatus of claim 11, wherein the processor is further configuredto: calculate, when the error approximation exceeds the threshold value,the mean revenue per impression of the corresponding media cell based ona relationship between a plurality of attributes of one or moreadditional media cells and an estimated mean revenue per impression ofthe one or more additional media cells.
 16. The apparatus of claim 15,wherein the processor is further configured to: determine a plurality offactors that describe a relationship between the attributes of the oneor more additional media cells and the estimated mean revenue perimpression of the one or more additional media cells, wherein each ofthe plurality of factors is associated with a corresponding one of theplurality of attributes; and calculate the mean revenue per impressionof the corresponding media cell based on a logarithmic-linearcombination of the plurality of factors.
 17. The apparatus of claim 15,wherein the plurality of attributes comprise at least one of a website,a slot size, or a segmentation model associated with each additionalmedia cell.
 18. The apparatus of claim 11, wherein the processor isfurther configured to predict the revenue per impression of the targetmedia cell based on a weighted average of (i) the estimated mean revenueper impression of the corresponding media cell and (ii) measurements ofrevenue per impression for the target media cell.
 19. The apparatus ofclaim 11, wherein the processor is further configured to adjust the meanrevenue per impression of the corresponding media cell to account forone or more of audience leadback and advertiser leadback.
 20. Atangible, non-transitory computer readable medium storing instructionsthat, when executed by at least one processor, cause the at least oneprocessor to perform a method, comprising: generating an approximationto an error associated with a mean revenue per impression of acorresponding media cell, the corresponding media cell sharing one ormore common attributes with a target media cell, and the errorapproximation being based on at least a number of impressions associatedwith the corresponding media cell; determining whether the errorapproximation exceeds a threshold value, the threshold value associatedwith a revenue model of the corresponding media cell; calculating, whenthe error approximation does not exceed the threshold value, the meanrevenue per impression of the corresponding media cell based on adistribution of revenue per impression associated with the correspondingmedia cell; and predicting a revenue per impression of the target mediacell based on the calculated mean revenue per impression of thecorresponding media cell.